According to Admiral William Daniel Leahy, he highest ranking member of the U.S. military at the time, "the use of [nuclear weapons] at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender".
The nukes were used not to beat the Japanese, but to intimidate the Russians, who had advanced as an industrial force as part of their fight against Germany.
The only ones who could tell if the Japanese were actually ready to surrender were the Japanese.
They refused to surrender after Hiroshima.
They refused to surrender after the U.S.S.R. declared war.
Finally after Nagasaki their cabinet deadlocked 2-2 on the decision to surrender. The Emperor himself broke the tie by deciding for peace (a decision which brought a minor coup of its own).
Adm. Leahy was correct if he was using Western logic and ideals. In fact it was clear since 1943 that Japan would be defeated and had to surrender or eventually lose the war.
He's also correct that it was of no material assistance compared to conventional weaponry. There were only so many atomic bombs available and the B-17s rampaging across Japan were certainly doing a fine job as well.
The part I don't understand is why he thought atomic bombing a city was barbarous, but firebombing Tokyo was how gentlemen conducted warfare. More Japanese died in a single firebombing raid than died in Dresden, Hiroshima, or Nagasaki.
This raid I mention occurred in March 1945 by the way, not August. In light of that it's hard to claim with a straight face that conventional weapons were forcing Japan to surrender before invasion of the Home Islands. They had every reason to surrender in March if that was their only tripwire to decide to do so.
http://en.wikipedia.org/wiki/William_D._Leahy#Atomic_bomb
The nukes were used not to beat the Japanese, but to intimidate the Russians, who had advanced as an industrial force as part of their fight against Germany.